July 1997

The Mid-Atlantic Technology Transfer Center, College Station, Texas,
has contacted NIST with a request for more details on a patent recently
given to an ITL mathematician. Alfred Carasso, Mathematical and Computational
Sciences Division, received a second patent for his method for digital
image restoration. The center wants to publicize the invention in their
widely disseminated newsletter.

Most image deblurring procedures impose smoothing assumptions on the
unknown image in order to stabilize the ill-posed deblurring problem. However,
in many important industrial, military, surveillance, or biomedical applications,
the desired image is highly non-smooth, and reconstruction of fine detail
is of prime interest. The use of smoothness constraints, required by the
methods of the first patent, is particularly ill-advised in medical image
deblurring, as this might result in an oversmoothed image in which vital
diagnostic information regarding tumors, microcalcifications, and the like,
have been eliminated.

The method is one of 56 technologies, culled from a database of 11,000
emerging technologies, that was recognized as significant for future work
in an Institute of Defense Analyses report entitled "Information Warfare
Technologies: Survey of Selected Civil Sector Activities" by W.J.
Barlow and R.D. Turner, dated February 1996 (IDA Document D-1792).

The NIST procedure is based on a new "slow evolution" constraint,
which effectively constrains the known blurring kernel, rather than the
unknown solution. Since no smoothness constraints are imposed on the image,
the procedure is highly effective in reconstructing fine detail. A rigorous
analysis of this method appears in the SIAM Journal on Mathematical Analysis,
Volume 28, Number 3, May 1997, pp. 656-668. Images deblurred via this procedure
have been shown to have higher resolution than those obtained using non-linear
probabilistic approaches such as the maximum entropy method, the Lucy-Richardson
method, or the maximum likelihood E-M algorithm, while using far less computer
time.